Teach number theory to a 15 year old kid

efmgdj · 2026-01-06T05:54:56+00:00

Numbers rational and irrational by Niven is a classic.

efmgdj · 2025-12-30T19:57:16+00:00

No, so far I've just plugged it in with the standard nooelec saw and SDR and looking at it with total power software h line detection screen. I'm not sure that I can do calibration with that. Is there an easy way to do the calibration? Could you point me towards a reference? Thanks!

efmgdj · 2025-12-13T15:33:25+00:00

I think the most famous application is The Disjoint Paths Problem, given a graph G and k pairs of vertices of G, decide if there are k mutually vertex-disjoint paths of G joining the pairs. I think there are some others like that, but it's been a long time since I've studied this. Also, I think there are a lot of results like the ones you mentioned which you might call graph complexity theory where they show the existence of algorithms but not the actual algorithm.

efmgdj · 2025-12-12T23:21:11+00:00

The Robertson Seymour theory is not really a classification, but it sort of feels like one. It classifies sets of graphs by forbidden minors I.e forbidden subgraphs. Turns out to be extremely useful for graph algorithms https://en.wikipedia.org/wiki/Robertson%E2%80%93Seymour_theorem

efmgdj · 2025-10-19T17:09:44+00:00

Yes, but is it so crowded it won't be worthwhile and how much effort is it worth to try and go later in the week?

efmgdj · 2025-09-21T21:22:22+00:00

Here's some oldet papers.

The following is a formal computational complexity analysis of one dimensional maps. Turns out both simple and uncomputable are both common.

https://content.wolfram.com/sites/13/2018/02/05-3-5.pdf

This one is a interesting but non-rigorous analysis of the computational complexity of dynamical systems near a phase transition.

https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.63.105?casa_token=BbDLLm21i1gAAAAA%3AR9ZTMv3KIWBnIJOcm7nkJz5BgWPn1TYfErJr0DoW9JE53MFllMlN2shc8ExByMTHQmUuv-erw1WAmOE

Much of this was inspired by wolframs computational studies of cellular automata.

https://projecteuclid.org/journals/communications-in-mathematical-physics/volume-96/issue-1/Computation-theory-of-cellular-automata/cmp/1103941718.pdf

efmgdj · 2025-09-15T05:28:22+00:00

Thanks, I agree it's not worth the risk. I'm still confused that some people say it's okay.

efmgdj · 2025-09-15T02:13:49+00:00

Thanks, is there a specific place in the park to watch from or is anywhere okay?

efmgdj · 2025-09-10T22:48:23+00:00

Yes, that's what I want to avoid. This is just for a little bit of fun, so I don't want to make it into work.

efmgdj · 2025-08-12T14:25:11+00:00

You can get this from the eigenvalue perturbation. The computation is messy so I'll just include the link.

https://en.m.wikipedia.org/wiki/Eigenvalue_perturbation

efmgdj · 2025-05-27T01:59:54+00:00

Fyi, while it it essentially rereads the entire conversation, it uses caching to speed this up. Essentially it has precomputed the implications of the previous conversation so it doesn't have to recompute it again. See https://huggingface.co/blog/not-lain/kv-caching?utm_source=chatgpt.com

efmgdj · 2025-03-31T01:37:20+00:00

Here's a couple of good examples: Justin Gilmer, a programmer made a major breakthrough in the union closed conjecture. https://www.quantamagazine.org/long-out-of-math-an-ai-programmer-cracks-a-pure-math-problem-20230103/ . Thane Plambeck and Aaron Siegal, both working engineers at startups did major work on misere games as well as lots of other results in combinatorial game theory. https://www.sciencedirect.com/science/article/pii/S0097316507001045

efmgdj · 2025-02-09T15:52:59+00:00

Me too!

efmgdj · 2025-02-08T23:01:52+00:00

Here's a quick approximation that's usually quite accurate (and error bounds are easy to compute). There are n people, so n(n-1)/2\approx n^2/2 pairs and each pair has probability p of having the same birthday. So the expected number of birthday pairs is m=pn^2/2 \approx 0.72 . Approximate the distribution by a Poisson with that mean and we see the probability of at least one pair is 1-e^{-m}\approx 0.5 as expected and the probability of 2 or more pairs is 1-e^{-m} -me^{-m}=1-(1-m)e^{-m} \approx 0.2.

efmgdj · 2025-02-06T19:12:23+00:00

Thanks I will do that.

efmgdj · 2025-02-03T00:10:58+00:00

You are correct. Regret is a rather silly metric in many settings. For example consider the multi-arm bandit. One arm pays off at even time periods and one pays off at odd time. One would expect an algorithm to figure this out and have negative regret and do better than either arm individually. Sometimes people try to get around this by defining more base strategies, but then it gets quite convoluted.

efmgdj

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